Suppose that 14 overweight individuals are divided randomly into two groups, with 7 in each group. The first group is assigned to use a diet intended to cause weight loss, and the second group is assigned to use an exercise plan to lose weight. After three months, weight losses (pounds) in the two groups are as follows:
Diet plan: 10, 8, 12, 16, 0, 7, 35
Exercise plan: 12, 7, 2, 3, 5, 4, 9
a. Find the value of W, the test statistic for a two sample rank-sum test that would compare the two methods for losing weight.
b. Carry out a two-sample rank-sum test (Mann-Whitney-Wilcoxon test) in which the alternative hypothesis is that median weight loss is greater if dieting is the weight-loss method used.